This paper presents a complete review of the significance of deterministic mixed-integer linear program (MILP) and mixed-integer nonlinear program (MINLP) solution methods for problems involving linear, nonlinear, convex and nonconvex functions. The mathematical description of methodologies, algorithms, software, and solvers to solve this problem are presented. Mixed-integer program (MIP) problem is one where some of the decision variables are constrained to be integer values. MILP involves problems in which only some variables are constrained to be integers, while other variables can be non-integers. It deals with linear objective function subjected to linear constraints. Minimisation and maximisation of a nonlinear objective function subject to nonlinear constraints with continuous and discrete variables are performed by MINLP solution methods. In this paper, the recent MILP and MINLP solution methods, algorithms along with solvers and software, introduced by various researchers has been elaborated profoundly. © 2020 IJSTR.